With an inverse graphics model, PromptGen can control the pose of faces generated by StyleGAN2.
We used the DECA model [1]},
which infers the parameters of FLAME [2]}, a parametric facial graphics model.
We set \(\mathbf {\rho } \in \text{SO}(3)\)  as FLAME's three neck poses and used the conditional INN extension introduced in Section REF .
To enable generating different poses of the same identity (ID), we propose ID energy using the IR-SE50 model [3]}.
Specifically, given a canonical pose \(\mathbf {\rho }_0\) , we define \(\mathbf {z}_0 = f_{\mathbf {\theta }}(\mathbf {\epsilon }, \mathbf {\rho }_0)\) , and the ID energy is defined as (detailed in Appendix REF )
\(E_{\text{ID}}(\mathbf {x}_0, \mathbf {x}) = 1 - \cos \big \langle R(\mathbf {x}_0), R(\mathbf {x})\big \rangle , \quad \mathbf {x}_0 = G(\mathbf {z}_0), \mathbf {x}= G(\mathbf {z}),\) 
